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What are the most popular areas to do private pilot flight training in the United States?
Are there any statistics on the most popular states to do private pilot flight training in the USA or a similar measure?
I know Florida is very well visited, but I was wondering if there were other states which also have high number of students.

By statistics do you mean number of student pilots getting enrolled, or percentage of students getting their PPL?

Enrolled students would be great :)

The FAA has a document on their website which breaks knowledge tests down by FSDO rather than state, and it gives a good idea of where the most training is taking place.
It is called: 2013 Airmen Knowledge Tests by Region and FSDO, and lists the following Regions/FSDO's as processing the most knowledge tests (in descending order)1:

Southern 28,333
Orlando 9,996
South Florida 5,958
Alabama & NW Florida 4,680
Atlanta 3,882
Tampa 2,504
Western Pacific 18,416
Scottsdale 6,053
Riverside 1,556
San Diego 1,463
Sacramento 1,460
Long Beach 1,327
Fresno 1,270
Los Angeles 1,142
San Jose 1,121
Southwest 15,943
Dallas 2,731
Fort Worth 2,581
Houston 2,438
Oklahoma City 2,347
San Antonio 2,321
Eastern 14,552
Richmond 1,956
Greensboro 1,366
Farmingdale 1,280
Philadelphia 1,198
New York City 1,069
Boston 1,041
Great Lakes 11,860
Fargo 2,120
Dupage 1,414
Indianapolis 1,358
Minneapolis 1,142
East Michigan 1,111
Northwest Mountain 9,784
Denver 2,205
Portland 2,131
Salt Lake City 1,964
Seattle 1,611
Central 9,019
Nashville 4,293
Wichita 1,304
Alaskan 812

Based on this data, I would say that the areas surrounding the Orlando, Scottsdale, South Florida, Alabama & NW Florida, Nashville, and Atlanta FSDO's are the most popular training areas, with the Southern region being the most popular by far.

1 To improve readability, all FSDO's with less than 1,000 tests have been removed.  See the source data for the complete list.

Excepting Alaska with only 812 State-wide.

There are two popular areas:  1) Where you live.  Most pilots desiring to fly for fun train near their home and family, and 2) Where the weather is good.  aka somewhere down south, Arizona and Florida are the most popular.  Why?  Fewer no-fly days.  There is a reason that ERAU has branches in Florida and Arizona.

I used to train in the Phoenix area. Very busy. Lots of Chinese, Vietnamese, Dutch, Germans, Englishmen etc. (CAE Oxford, KLM Flight Academy (although I believe they recently ceased their training facility there) and many others. I'm sure this will not satisfy as an answer since these are all CPL training facilities and not PPL. Thought it would be interesting to share though. Cheers.


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How effective are modern aircraft at clearing smoke?
In reference to this incident by a certain (in)famous artist, i'm wondering how effective modern aircraft are at clearing smoke for single aisle commercial aircraft such as B737/A320 or a business jet like in the story?

Which direction does the airflow in a cabin move? Top to bottom?
How far are people effected by secondhand smoke if somebody lights a cigarette? Would it be within a one-meter range or would people notice across the whole cabin?

After those pilots donned their masks they should have depressurized the cabin LOL. It would have purged the smoke and shut that kid up real quick. Could wake him after the flight..

It seems like this would vary greatly depending on the aircraft in question.  What plane do you mean?

like a320? i would imagine there's a airflow requirement perhaps?

You may be asking about smoke in the cabin, but I thought of pointing a jet engine at a fire to blow the smoke away...

The most relevant data I could find was located here, in a study on "In-flight cabin smoke control". In the abstract, they stated that

Tests on a Boeing 757, modified to allow smoke venting out through the top of the cabin, showed that the buoyant smoke front moved at 0.46m/s (1.5ft/sec) with and 0.27m/sec (0.9ft/sec) against, the axial ventilation airflow. Flight tests in a modified Boeing 727 showed that a ceiling level counterflow of about 0.55m/sec (1.8ft/sec) was required to arrest the forward movement of buoyant smoke. A design goal of 0.61m/s (2ft/sec) axial cabin flow would require a flow rate of 99m3/min (3500ft^3/min) in a furnished Boeing 757. The current maximum fresh air cabin ventilation flow is 78m^3/min (2756 ft^3/min).

In short, during continuous generation of smoke, cabin air will not be recirculated quickly enough to stop smoke from filling the cabin; however, if the smoke production is temporary, then it should dissipate quickly (time of course depends on the size of the cabin and the amount of smoke produced).
On page 2 of this article, a discussion of airflow occurs and contained this image, showing circulation patterns on wide-body airliners. A linked study on that same page noted that an under-floor displacement air distribution system [like the commonly used type picture below] can provide a much better air quality than a mixing air distribution system. The paper goes on to provide more diagrams of airflow and comparisons of various effectiveness if you're interested.

Boeing has a fairly detailed summary of their cabin airflow here. It says:

Inside the cabin, the air flows in a generally circular patterns and exits through floor grilles on either side of the cabin and on airplanes with overhead recirculation, the air may exit through the overhead. The exiting air goes below the cabin floor into the lower lobe of the fuselage.

So at least on most Boeing planes, air exits at your feet, though it can exit at the ceiling. Airbus also has a page here, but with much less detail. Airbus claims a complete recirculation every 2 to 3 minutes, while Boeing merely states airflow is continuous. The article linked below says in general, airplane recirculation occurs aproximately 20 circulations per hour.
An NBC article on cabin air states that to pick up a sickness, you need to be close, usually within two rows. The article goes on to say that:

The aircraft is divided into ventilation segments of three to seven rows; you share air only with passengers in your segment.

So presumably if there were smoke, it would be captured in a small area were it not too pervasive.

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Is there a best-practice method to work through a checklist?
I've noticed that there appear to be many ways to read of a checklist between aircraft types and operators. The task and work division confuse me:

In some cases it appears to be entirely managed by the Pilot Not Flying [PNF], while in some cases the Pilot Flying [PF] is involved.
For the latter case, the response from PF seems to be 'checked' some of the time while in others there is a verbal feedback on the state of that control.

I guess this is a question between Standard Operating Procedures, but is there a best-practice to reading off checklists that is suggested to be followed as suggested by EASA or the FAA for instance?

Extra Thing: It would be great if somebody could elaborate on how a checklist actually would be worked through in practice like the one below with who says and does what.

One at a time and try not to skip any?

The current FAA Advisory Circular dealing with SOPs in general, but only lightly touching upon checklists, is AC 120-71a. It is primarily aimed at Part 119 certificate holders who conduct operations under part 121, but is also recommended for operations under Parts 91, 125, and 135. It also changes the wording from Pilot Not Flying (PNF) to Pilot Monitoring (PM) in order to reinforce the idea that he or she is not just a passenger with a better view, but an integral part of the flight crew.
With respect to actual checklist usage, to the best that I've been able to find, the FAA does not issue a hard recommendation (air carrier checklists and procedures have to be approved by the FAA prior to certificate issuance anyways), but it does identify two primary methods of checklist usage: Challenge-Do-Verify (often used for abnormal and certain emergency procedures) and Do-Verify (often used for normal and time-critical emergency procedures), which relies on memorized flows followed by verification with the use of a checklist.
A 1995 Study issued by the FAA weighs in on the pros and cons of the two methods and surmises that, when used properly, the CDV method is less likely to result in missed items, but does allow for the fact that, in operational usage, pilots may batch items together, thus defeating the purpose of the systematic, step-by-step approach of the method.
Stepping aside from the multi-crew environment, where having someone with the checklist in their hand and reading things off one by one can work quite well, my personal observation has been that, in a single-crew environment, pilots who rely on a CDV-like method (sometimes known as Read-Do) are more likely to end up falling behind in configuring their aircraft than those who use DV-like methods, assuming of course that the pilots actually know their flows and perform the verification properly (as in actually verify that everything is as it should be rather merely reading items off the list and trying to remember if they've accomplished them).
Lastly, with respect to the 'checked' vs. verbal confirmation of status, this is usually dependent on how critical and laborious the status confirmation is. An example would be with altitude setting verification, where it is not uncommon for the procedure to call for the PF to set the new altitude in the Mode Control Panel and, while pointing to it, call out the new altitude, which is then verbally confirmed by the PM. Every operator's experience and demands will be different here, but a number of best practices are recognized and the folks at the FAA, NBAA, FSF, AOPA, and many others are doing their best to publicize and promote them.
See here for the FAA's Industry Best Practices Reference List.
The checklist you've provided appears to be intended for multicrew operations. In this particular case, what would happen if the CDV method was to be used is that the Pilot Monitoring would read the items off one by one and the Pilot Flying would execute accordingly, verbally acknowledge doing so, the PM would quickly verify compliance and move on to the next line item.
In a DV environment, the Pilot Flying would go through the flow, and call for the checklist, at which point the Pilot Monitoring would begin to read off the items, and the Pilot Flying would verify that they have been complied with.
The line items that have BOTH in them are meant to be a special emphasis case in that both crew members are required to verify that the line item has been complied with, regardless of method used.

There are really two aspects to your question: Operational usage and Design usage. The two are closely related, but let's look at them separately:

Operational Usage
From an operational standpoint the absolute best way to use a checklist is in a multi-person crew situation: Actions are performed (usually with the help of flows), then the checklist is read and each item is verified, ideally by a different crewmember than the one who performed the action.
This use of checklists provides independent and redundant verification that all required actions have been performed, and you find it in a lot of other industries that use checklists: The operating procedures at my day job are regulated by a different three-letter "F" agency, but our critical procedures still have checklists, and they're used as I described.
In a single-pilot environment the same logic holds: You generally want to use the checklist to verify (check) that things have been completed rather than using it as a "to-do list". This makes it a verification step and introduces redundancy into your procedures.
(If you can stand Jason Miller's slightly-cheesy intro music he discusses this in one of his podcast episodes, it's worth a listen.)

Design Usage
This is one that doesn't get discussed often, but ratchet freak made mention of it: Your checklist should be logically designed so you can move through it in an organized way.
The checklist you posted is an excellent example of this: A flight will proceed through that checklist top-to-bottom, left-to-right (the first things you do will be "Before Start", and the last things you do will be "Securing"), and within each category the checklist should also proceed in a logical order (for example good preflight checklists usually take you around the plane in an organized path.)
There is no shortage of badly designed checklists (manufacturer's checklists tend to be among the worst in this regard: A Piper or Cessna preflight checklist in the POH usually has you making 4 or 5 trips around the plane checking things in seemingly-random order).
The process of designing a good checklist is an interesting Human Factors problem - there's a lot of literature on it but it's way out of scope for this site. The usual solution to badly designed checklists is that pilots get frustrated and write our own.

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Is there anywhere I can pick up raw flight data recorder information?
We were plotting flightpaths as practice in programming class but unfortunately that was limited to some recordings from a research aircraft.
I'm wondering if I can pick up the raw data files from (accident) Flight Data Recorders somewhere to see if I can plot them as well?
(Like a file with rows listing time, position, altitude, airspeed etc.)

you could ask the FAA or NTSB for the raw data of some, no guarantees though

I'm thinking a FOIA request might be the way to go, but I don't know if it could be denied on the basis of containing proprietary airframe/engine manufacturer data. Wild speculation here.

@dvnrrs i'm just looking for those 88 FDR parameters, so I hope not. Seeems that the way to go is to send something off to some agency on some recent event (BA38 perhaps?) where it may be directly accessible on computer to see if they return something...

Just fired off a request to the AAIB for information about BA38. See if it returns anything...

You could use ADS-B recordings to plot the paths. I can provide you with tons of them if you'd like. I have recordings of PH-LAB as well so you can compare (I assume that is the research aircraft you are referring to)

@DeltaLima thank you, got several of PH-LAB as well, but thought it might be fun to try and graph engine parameters or something similar :)

Unlike the AAIB, the NTSB does release FDR data dumps (adjusted for engineering units and culled to the same parameters as the graphs) as part of the docket release for a given accident -- no FOIA pestering needed!
See these examples from the Bedford, MA Gulfstream overrun crash, for instance (they're CSV files).  You'll be able to find more by looking through the dockets associated with recent major NTSB accident reports.

If you want data from small aircraft, cirrusreports.com has data recorder information for thousands of flights. I don't believe you can actually download the raw data, but you can interactively plot dozens of parameters.

The AAIB responded quite quickly (and briefly) but were not very helpful:

AAIB does not release FDR raw data on any accidents in line with
  the EU regulation 996/2010 article 14.

Having a look at the corresponding EU regulation:

The safety investigation of accidents and incidents should be
  conducted by or under the control of an independent safety
  investigation authority in order to avoid any conflict of interest and
  any possible external interference in the determination of the causes
  of the occurrences being investigated.

Paraphrased, I don't think they want 'unexperienced' people interpreting data on their own and making conspiracy theories or something I guess :) That being said, the regulation doesn't expressly forbid the distribution of information in my opinion, but I won't bother discussing it further. I think that unless you have a proper reason for it, they won't give it to you.

Update: Paragraph 35 is interesting....

The rules on access to data, data processing and the protection of
  individuals laid down in relevant legal acts of the Union should be
  fully respected in the application of this Regulation.

which may imply that you could get it, depending on how those are written, which I have absolutely no clue about.


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Why doesn't Stratolaunch have connected tailplanes like it has connected wings?
As a complete layman, the design of the Stratolaunch airplane, especially when reminding myself of its size, seems too flimsy, in that the only connection between the two fuselages is the center wing. Apart from apparently trusting their materials and connections, what might the reasons have been for  Dynetics engineers to not also connect the tailplanes? Also, are there no aerodynamic disadvantages to having that many more trailing edges (if that's the terminology used)?

While I don't know, I'd guess that part of the answer is that it's supposed to carry a rocket vehicle underneath, and drop it to launch.  The separation between tails would allow for something like Sierra Nevada's Dreamchaser with its own vertical tail...

Interesting that neither of the two answers bring that up. Perhaps there'd be enough space even with a connection.

There is indeed an Eigenmode possible on the Stratolaunch which does not exist on regular airplanes: If the two fuselages pitch in opposite direction, thereby twisting the center wing. If that happens at the torsional eigenfrequency of the center wing, flutter might be possible.

Stratolaunch in flight (picture source)
Given the pitch damping of the horizontal tails, however, this scenario is rather unlikely. I bet the elevators have plenty of mass balance to avoid this flutter case. Underbalanced, their dynamic response would support flutter, but overbalancing would dampen this flutter mode. Connecting the tails would not make much of a difference and would even reduce pitch damping somewhat in the above mentioned case.
Similar configurations used both, a connection horizontal tail (F-82 Twin Mustang) or individual tails (He-111 Zwilling).

North American F-82 Twin Mustang (image source)

Heinkel 111 Z (image source)

I'm going to accept this for its use of comparison with other, past aircraft that illustrates the difference between the two design types real well. Also, I'd never seen either the F-82 or the 111 Z and had thought the White Knight to have been the first aircraft of this kind, so that puts things into perspective, too. Thank you, Peter!

The more I look at the Mustang, the more elegant it looks. And the Heinkel, while not as elegant, must have been quite the feat back in the day. According to Wikipedia, pilots apparently liked the Zwilling quite a lot. Do you have any idea how they achieved the structural stability necessary? I mean, what if there's a wind shear pulling on one tailplane and pushing the other - the torsional forces in the wing must get immense?

Wind shear is not so small-scale - this is not worse than with any other large aircraft. By giving the center wing a stiff skin, its torsional rigidity is sufficient for safe operation.

That's not how airplanes work. An airplane is the wing first, everything else just hangs on the wing in flight.
The correct way to look at an airplane is to imagine the wing without all the attachments, then add them one by one as weights. The engines are a semi-exception in that they also pull forward at their attachment points. The fuselages, on the other hand, are just fuel tanks, and also carry control forces from the tail surfaces.
Placing two heavy fuel tanks (fuselages) a considerable distance apart is much more structurally efficient for the wing than only placing one in the center. That's the reason it's done that way.
It's inefficient from the payload perspective (the payload, be it live or cargo, prefers one big tube), but the Stratolaunch carries its payload slung between the twin fuselages.
As for why the tailplanes aren't connected, the right question is "why should they be". There are multiple possible reasons for such a decisions, and a number of twin-boom aircraft where they are connected, often with a lifting surface that acts as a second wing. But the Stratolaunch is a twin-fuselage aircraft with conventional tails, and in this case it would cost a lot of extra weight to connect the tailplanes.
It's only on the ground that the aircraft rests on its wheels and the wing rests on the two fuselages. And indeed, a twin-fuselage arrangement does make ground handling more complicated, and on the ground the wing is subject to some forces arising from out-of-sync loads on the fuselages. But given this aircraft's mission, that's a minor concern.

Connecting the tails might help with managing twisting moments in case one of the rudder/elevator actuators fail in flight. But presumably they've modeled that and concluded the fuselage/wing connections are stiff enough to handle that load.

@qq, I bet they could fly it with rudders only for roll, and avoid asymmetric elevators.

Unfortunately one cannot accept two answers. Thank you as well, Therac, especially for approaching the question in a bottom-up, engineering, kind-of-way. FWIW, having this here adds to the one from Peter!

It’s mainly because the load is shared between two fuselages like in mechanics the load of a bridge is shared among its towers sharing the bending moments

Hi and welcome to the site! This doesn't seem to address the question, which is about the tail planes as opposed to the wing. The airframe would, at first glance, gain stiffness if the tail planes were to be coupled.

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Do box-wings suffer from induced drag the same way as normal wings?
Most wings suffer from induced drag due to a pressure difference above and below the wing causing air to sneak around the tip, forming a vortex. There are various methods to minimize these effects, such as winglets.
However, looking at the Synergy aircraft as an example, box wings have no wing tips. Disregarding any other parts of the aircraft, are the wings actually free from induced drag? Or are they still causing induced drag, just in a way I'm not able to think of with my limited fluid dynamics experience?

Synergy aircraft with box wings (picture source)
I've read somewhere that a traditional bi-plane design is less efficient due to the wings interfering with each other (apparently something addressed by the synergy aircraft by placing the upper wing further back or something), and the upper wing is actually more of a tail-plane, pushing down, thus further increasing the airspeed in between the airfoils if I understand correctly and eliminating the pressure differential from the top of the upper wing to the bottom of the lower wing, and both wings would of course generate normal drag by cutting through the air, but I'm only interested in the induced drag at this point.

looks like a fancy biplane-like design.

@ratchetfreak except bi-planes have four wingtips, this one has zero.

@falstro: This has two wing tips. The meaning of "upper" surface changes over the vertical struts, so they act as tips anyway (and if it didn't change, the upper surface would produce negative lift and the whole thing would produce none and be useless).

@JanHudec; actually the upper surface does produce negative lift (as I mentioned in the last sentence of the question), it sits behind the lower wing and works like the tailplane of other aircraft.

@falstro: Nevertheless since the whole thing produces net lift, it accelerates air downward and since the air beyond it's span is not accelerated, creates wingtip vortices with the vortex lines leaving the system somewhere along the vertical struts.

Their website says it's not a box wing, and the two upper horizontal surfaces are tails, and generally provide downwards force.

The box wing is only better when you compare wings with identical span. The two wings of a box wing work in different Treffz planes, so the downwash is spread out vertically. The difference in induced drag to a single wing is not big, just a few percent. The friction drag is higher (see below), as is the structural mass, so the box wing needs to create more lift. This makes the induced drag of a box wing effectively higher than that of a single wing.
What is induced drag, anyway? It is the consequence of creating lift over a limited span. The wing creates lift by deflecting air downwards. This happens gradually over the wing's chord, and creates a reaction force orthogonally to the local speed of air. This means the reaction force is pointing up- and slightly backwards. This backwards component is induced drag! Wingtips are not involved and are not causing induced drag. Lift creation is.
If you fly fast, there is a lot of air mass streaming past the wing per unit of time, so you need to deflect the air only slightly. Your induced drag is small. Sames goes for a large span: There is more air which can be deflected, so the induced drag is small.
A box wing needs two slim wings per side, which will have a smaller chord than a single wing of the same surface area. So their Reynolds number is smaller, and their friction drag is higher. Also, the wing spar is less thick and will need to be heavier to carry the same lift!
If you drop the restriction of keeping span identical, the optimum single wing can afford to have more span (due to its better structural efficiency), and away goes the advantage of the box wing. And once you look at the full picture and add structural mass, the box wing never had this advantage in the first place.
Yes, but what about the Synergy?
The Synergy is a clever design with some advantages, but it cannot cheat physics. These are the advantanges:

The pusher prop keeps the airframe free of wake turbulence, so more area can be kept in laminar flow.
The pusher prop sucks the air from the rear fuselage, effectively avoiding separation.
The two stubby tailbooms and fins give great protection for the propeller area on the ground.
The compact layout keeps the stabilizing effect of the propeller small, so maneuverability does not suffer much.
The use of composites and glider airframe technologies reduce friction drag.
The diesel engine consumes cheaper jet fuel and is more fuel-efficient than a gasoline engine.

Note that I did not mention the box wing design?
Here are the disadvantages:

Wing sweep in a propeller aircraft looks cool, but increases drag, because the wing must be bigger to create the same lift.
In total, this configuration has four vertical tails, each of them with its own interference drag and a short chord which, again, increases drag over a comparable single vertical tail.
The stretched-out horizontal tail is also less effective than a smaller single surface with more chord and more distance from the center of gravity.
The compact layout provides little pitch or yaw damping. I wonder what the ride qualities in gusty weather are.

I would expect that a more conventional layout along the lines of the fs-28 would be even more efficient.

Akaflieg Stuttgart fs-28 in flight (picture source)

Did Wikipedia have an article on the Trefftz plane back in the day? At any rate, that link is effectively dead, just fyi.

@AEheresupportsMonica: Thank you for letting me know. I cannot remember what the Wikipedia page looked like 5 years ago, but now MIT has a much better page up which shows what I mean.

Q: Do box wings suffer from induced drag the same way as normal wings?
A: Yes and no. Box Wing aircraft will suffer from induced drag the same as any aircraft will, if they are heavier-than-air vehicles and are using their wings to fly. Induced drag is a function of finite span loading, and moderated by various ways to improve design efficiency at a given span loading. Thus the amount of drag, and the way it is created and avoided, differs for a boxwing and a monoplane of the same span. Today this topic of induced drag includes completely different definitions than what was taught in seminal references on the subject. Even if one is talking about the same thing, the topic will hear arguments from two different camps: those who adhere to representative mathematics, and those who focus on the non-Cartesian, non-textbook actual physics on a case-by-case basis. It's quite fair to say that the former are more vocally opinionated than the latter, for the latter know less until later.
The job of a wing is to efficiently push and pull air downward as it moves forward. That action causes both a Newtonian reaction and a Bernoulli pressure differential, resulting in lift.
Making lift this way causes the nearby air to also be affected, as a time-dependent secondary result. It has to 'fall into the descending trough of air' that the wings displaced downward.
This secondary movement causes (completely unavoidable) rotational movements in the "wake" zone between air directly moved by the wings and the nearby stationary air, thereby involving more air mass than the plane needed to move just to get the lift it needed. (The momentum difference is quite literally the induced drag, although we usually teach it in ways more related to how induced drag is visualized and computed in 2-D. Other answers posted here illustrate this in conventional terms.)
Induced drag and wake vortex CANNOT be eliminated for a lifting wing system of any kind. However, most aircraft wing designs allow something else to happen that greatly increases this cost of making lift with a finite wingspan: they let high pressures under the wing be 'too close' to the low pressures above the wing for the amount of pressure difference that has developed in flight. If a high differential pressure exists at a wing tip, a strong, tornado-like vortex will form there.
Allowing any strong gradient to form between low pressure and high pressure will cause air to move toward the low pressure at a high velocity, if it can. Drag increases exponentially with the velocities imparted to the air, therefore designers use a variety of approaches to keep this equalization from happening quickly. The slower it happens, the less kinetic energy is imparted to the air by the airplane.
This is where Boxwings have a totally different way of reducing the induced drag, compared to a normal wing: they put a wall up between the low pressure above the wing, and the higher pressure everywhere else. The 'wall' can be taller than a winglet, because it has a wing above to help resist the forces that push on it from the side. At that upper wing connection, the wall-like vertical surface of a boxwing likewise stands between the higher pressure under the wing, and the lower pressure everywhere else.
If a designer does a good job with this idea (many do not), both the biplane wing surfaces and the vertical surfaces of the boxwing system will moderate the velocity of gradient-induced airflows by acting against the undesirable flows in 3-D space. They become more effective in this with greater vertical spacing.
The easier and more effective way to reduce the induced drag is simply to increase the wingspan, or reduce the vehicle weight. As a wing gets longer, the portion of the lift each unit of the wing needs to make is reduced, meaning that it will have a lower pressure differential between the upper and lower surfaces. Best practice calls for this differential to be minimized at the tip, so the gradient is weakened. The result then is that a weaker pressure gradient and a longer distance between low and high pressures will keep the equalization velocities down.
However, as an aircraft gets heavier or goes faster, this approach becomes first very expensive, then impossible. Material strength limitations put definite limits on the wingspan of conventional aircraft.
Surprisingly, box wings fare no better... perhaps worse. What appears to be a structural advantage actually merely concentrates the bending forces, generated by each wing, into the corners of the box. Making them strong enough quickly becomes excessively heavy. Therefore, a box wing aircraft should, like a biplane, have a shorter span than a monoplane of equivalent induced drag. Its span efficiency bears greater fruit among short span designs, than where wingspan can be increased.
One might think that this advantage would then bear fruit indirectly, through speed. The faster an aircraft flies, for a given span loading, the less induced drag it will make. In fact, at high indicated airspeeds, induced drag becomes a small component of total drag. However, other aspects of box wing designs seem to have impeded high-speed boxwing solutions; notably stability; and "interference drag."
In a box wing design, there is a forward set of lifting wings, and an aft set of lifting wings. In high speed flight this configuration cannot respond as stably or as quickly to certain conditions as a wing with a (downward-lifting) tail.
When set up as a tandem-lifting wing arrangement without such a stabilizer, as is typical of modern versions, boxwings have to balance at their combined center of upward lift, rather than ahead of it like conventional aircraft do, thanks to the stabilizing influence of a tail pushing in the opposite direction. This limitation and tandem-wing stall behaviors place challenging, inherent demands on boxwing designs that constrain their success at higher flight speeds.
As noted above, they also create interference drag. This type of drag can be hard to predict and is also widely misunderstood. In practice, the inherent, 3-D interference drag of a boxwing aircraft design greatly reduces the 2-D theoretical advantage of the configuration toward obtaining induced drag benefits. This is why they are not at all like "normal wings."
As mentioned in the original post, there is a new aircraft configuration that is often mistaken for a box wing design. However, it is nothing like them. It's called a box-tail or double boxtail configuration. I am the designer of the Synergy double boxtail aircraft, which is the first such aircraft to be developed.
These somewhat disappointing attributes of the otherwise logical box wing configuration were at the heart of matters during the long period of Synergy's development. It was my desire to utilize high span efficiency and laminar flow in a high speed aircraft design, while avoiding high speed landings and unpredictable, unstable behaviors at low speeds. A video of a 25% scale model in flight and a basic overview can be seen at synergyaircraft.com. A post on the topic of boxwings can be found there as well.
For more information regarding span efficiency and non-planar configurations, Ilan Kroo has published very thorough overviews of the subject. The graphic below is adapted from one appearing in his papers. It shows how induced drag can be fought in 3-D space by moving away from a flat, planar wing into the vertical dimension. Synergy builds that understanding further, into the longitudinal and time dimensions, in accord with the concepts advanced first by George C. Greene while at NASA Langley.

You start with a great explanation of why induced drag happens, only to fall into the old trap of "vortices created by flow around the tip" as most others here do. Sad.

@Peter I think you're being a tad pedantic here (which would be OK if you did not call it 'sad'). While it's true that vortices are not the cause of induced drag, one can show that lift generation without vortices would be equivalent to creating lift with an infinite wingspan. Like many things in physics, cause and effect are largely dependent on ones viewpoint rather than an absolute measure.

@sanchises: I agree. Yes, I am pedantic, but only because I am convinced that only rigorous logic will lead to a complete understanding. Muddled thinking where cause and effect become interchangeable will lead to muddled understanding, and explaining something from that starting point will do a disservice to novices who will so easily misunderstand the details. And then you hear again from these poor people which never got a chance to learn things properly that the tip vortices cause drag. Isn't it right to feel sad about this?

@PeterKämpf But then, being too focused on rigor leads to needlessly complicating things. Reducing wingtip vortices does lead to an increased effective wingspan reducing induced drag - so perhaps as a rough approximation, saying "wingtip vortices cause induced drag" does have a core of truth to it. But I guess as with anything in aviation, the 'simple explanation' indeed holds relatively little explanatory power, and will fall short when box wings are analyzed in detail.

They're not free from induced drag, but the induced drag is greatly diminished, as demonstrated in Prandtl's NACA paper from 1924 and reported in this book (See chapter 11)

The authors of that book applied the results to the design of this aircraft

Cool! So where does the induced drag come from?

@falstro the wings will never be perfect, some circulation will still happen. Also, the aerodynamic force vector, depending on the wing shape, can be slightly tilted backwards, creating a drag component.

wikipedia has some schematic that let C wings approach box wings

@Federico: The circulation around the tips is some percent. Perhaps 10 or 20 %, but not more. Most is caused simply by applying force on air and the air, being freely movable, accelerating and taking kinetic energy with it. Nothing can be done about that. Result is that the induced drag is diminished, but not greatly.

@JanHudec I have difficulties understanding what you mean, but if I read you correctly, you speak about the whole drag, not the induced part alone.

@Federico: I am only talking about induced drag.

@Federico: On a side-note, induced drag is the dominating component of drag at slow speeds up to $V_Y$.

@Federico: Read the other two answers. They are both saying the same thing in different words.

Note, that the paper you quote explicitly compares to "monoplane with the same span". A monoplane with longer span will produce less induced drag.

The main reason for induced drag is, that the wing accelerates the air above and below it downwards increasing it's kinetic energy and due to law of conservation of energy, it has to take that energy somewhere and the only way is by doing negative work on the aircraft, i.e. inducing drag.
The amount of air accelerated per unit of time is proportional to the wing span and speed of the aircraft. Applying the same force to more air accelerates it to lower speed and because kinetic energy is proportional to square of speed it induces less drag. That's why high aspect ration (long span) wings are more efficient and why induced drag decreases with speed.

The wingtip vortices are simply borders of this area of descending air. And because you can't generate lift without accelerating air downward (by law of action and reaction), this induced drag is principal and any finite-span wing will induce it . And it will only depend on the lift generated, wingspan and speed and nothing else.
See also How It Flies, section 3.13 (the figure is from there).
Now there is some additional induced drag caused by higher-pressure air flowing around the wing-tip which does not contribute to lift (or even slightly negatively), but contributes to drag. It is maybe low tens of percent or something like that. The several percent that can be saved by various measures are significant enough to be worth the effort, but they are still several percent. Miracles are not possible.
By the way, the box wing still has tips. Air can't flow to or from between the wings, but it can flow from under the lower horizontal surface to above the upper one. Plus the wing is relatively low aspect ratio.

Many good points about drag reduction here.
Yes, induced drag can be reduced a few percent with a box wing, by diffusing the wing tip vortex.  Makes a difference of a few percent, which is significant.  About the same as a biplane.
The REAL compelling advantage of boxwings is structural.  With the wings connected at the tips, it's possible and practical to design for a given strength and rigidity with less material.  The wings can support each other, and damp each others natural resonance, buying some margin against flutter and failure.
Rick Gendreau,
designer, Halcyon boxwing.

Induced drag is generated as energy is lost in the wake. In order to create lift, air needs to be accelerated downwards (F=m*a). This means that after the aircraft passes, the previous stationary air, now has a downward velocity, so kinetic energy. This is regardless of the method of creating lift, or how many tips the wing have or doesn't have. Actually, wing-tip vortices are called like that because they are formed at the wing-tips, but the fallacy is - the vortices are not generated by the wing-tips. Any device inducing fluid movement will generate "wing-tip vortices" at the moving-stationary fluid interface, regardless of having or not wing-tips. Any undergraduate aerodynamics student should know this. Look at the Trefftz Plane Theory to get more details.

Closed systems (Box Wing is only a particular type of closed wing), C-wings and biwings are actually related as far as the minimization of induced drag is concerned.
If you are interested in technical answers regarding the induced drag minimization/performance of Box Wings, closed systems, bi-wing systems, and multiwings, you can find all the details in the following publications (I can also send to you the papers if you email me at the address luciano.demasiATgmail.com):
=====Article 1 =====
Demasi Luciano, Monegato  Giovanni, Dipace  Antonio and Cavallaro  Rauno "Minimum Induced Drag Theorems for Joined Wings, Closed Systems, and Generic Biwings: Theory", Journal of Optimization Theory and Applications, 2015, pages 1-36, DOI: 10.1007/s10957-015-0849-y, ISSN:0022-3239
=====Article 2 =====
Demasi  Luciano, Monegato  Giovanni, Rizzo  Emanuele, Cavallaro  Rauno and Dipace  Antonio "Minimum Induced Drag Theorems for Joined Wings, Closed Systems, and Generic Biwings: Applications" Journal of Optimization Theory and Applications, 2015, Pages 1-25,Doi: 10.1007/s10957-015-0849-y, ISSN:0022-3239
=====Article 3 =====
Demasi  Luciano, Monegato  Giovanni, Cavallaro  Rauno "Minimum Induced Drag Theorems for Multi-Wing Systems" ,2016,4-8 January,SciTech2016, San Diego, California, AIAA 2016-0236
=====Article 4 =====
Demasi  Luciano, Dipace  Antonio, Monegato  Giovanni, Cavallaro  Rauno
"Invariant Formulation for the Minimum Induced Drag Conditions of Nonplanar Wing Systems", AIAA Journal, 2014,October,10,2223-2240,52, Doi:10.2514/1.J052837
Url: http://arc.aiaa.org/doi/abs/10.2514/1.J052837

The references are certainly helpful, but including some information here in the answer would be even more helpful.

You can find more information on wikipedia at the following link:
https://en.wikipedia.org/wiki/Lift-induced_drag
[several pictures are also posted there]
Or I can send material if you provide an email address.
Best regards,
Luciano Demasi


text:
If I fly both Part 135 and Part 91 in a 24 hr period, which regulations apply?
I was wondering if there is a regulation if you fly both part 135 and part 91 in the same day which regulations do you follow?

Regulations in regard to what? Crew hours? Rest periods?

Welcome to aviation.SE! I'm not sure what you're asking here. As Ron said, are you asking if part 91 flights count towards part 135 flying time limits? Or are you asking something completely different? If you can be more specific then we may be able to answer.

Part 91 contains the General Operating and Flight Rules. These rules apply to almost every civil flight within the USA.
Part 135 contains the Operating Requirements for Commuter and on-demand operations and the rules governing persons on board such aircraft.
So when you fly the "Part 91 flight", you follow the regulations of Part 91.
When you fly the "Part 135 flight", you follow the regulations of both Part 91 and Part 135. If Part 135 is more strict in some regard, the more stricter rule of 135 applies.


text:
What aircraft has the highest critical Mach number?
What aircraft has the highest critical Mach number? The highest I heard of was BAC/English Electric Lightning at Mach 0.95. Are there planes with higher Mcrit. and is it plausible to go higher than that in a manned plane?
Note: Critical Mach number is the lowest flight Mach number when the speed of sound is reached locally on the airframe.

Yes, I definetly mean critical mach number. The title is odd, I know, that's for getting attention ':)

Then please ask precisely what you want to know. If you disagree with my editing, feel free to roll back, but be aware that you will risk to have the question closed.


text:
Is a winglet better than an equal span extension?
Is there indisputable evidence that a winglet improves performance over an equal span extension? Please note: I am only interested in L/D improvements.
Winglets do improve roll performance, that is not what I am looking for. Also, if span is restricted, winglets improve L/D over straight wings. Again, that is not what I am looking for.
Boeing and Airbus use fancy wingtip designs to demonstrate technological sophistication and make incredible-sounding claims about them. This is not the kind of proof I ask for. Is there theoretical or practical evidence comparing winglets with span extensions of equal wetted surface which show that the winglet produces better L/D values at any point of the polar?
Bonus points for a comparison of net lift to drag comparison, so the structural impact of both wing extension and winglet get subtracted from the generated lift. This should be the fairest way to compare both, but it seems such research is not published at all.

would you believe NASA?

@ratchetfreak: Yes, if they compare them to equal span extensions, which they do not in the linked page.

May I argue you should not focus only on L/D but take into account the construction weight as well. My feeling is that an equal span extension would generate a higher bending moment in the wing root, requiring a heavier construction. What you should compare is the "nett L"/D which is the aerodynamic lift minus the weight of the wing construction divided by the drag. That gives a fair comparison.

@DeltaLima: Yes, you are absolutely correct. But it is hard enough to find just a fair aerodynamic comparison. All papers look at the winglet in comparison to the naked wing, without extension. That's why I wanted to reduce the complexity of the problem.

and even if they weren't "better" for some aircraft increasing wing span is no option as it'd mean they wouldn't fit on taxiways and parking spots.

In the absence of a span restriction, the evidence is that a winglet is definitely inferior to a span extension of the same size when structural effects are included with induced, viscous and compressibilty drag.
The University of Michigan MDO (Multidisciplinary Design Optimization) Lab has done extensive research into the effects of structural weight in the optimization of wing lift/drag. Aerostructural optimization of non-planar lifting surfaces directly addresses this question. It describes a series of numerical optimizations on a b737-900 class generic aircraft with a NACA 64A212 airfoil, including the following representation of a structural model.

A gradient free optimizer is allowed to develop wing configurations to satisfy various constraints. The wing is represented by up to four segments. The geometry of each segment is defined by six design variables: span, area, taper,
twist, sweep and dihedral. Shown are four possible wing geometries.

For the aerodynamic optimization, box-wing or joined-wing
configurations were found to be optimal when only induced drag was
considered. When viscous drag was added, these configurations
incurred a drag penalty due to the large surface area, and a C-wing
configuration was preferred. The reduction in drag was similar for these cases, ranging from 26% for the joined wing to 22% for the C-wing configuration. Ignoring structural effects makes many solutions appear attractive.
Allowing the optimizer to perform trade offs between aerodynamics and structure is a significant improvement over previous approaches, where structural performance was considered by simply constraining the root bending moment. When structure, induced drag, viscous drag, and compressibility are all considered, a raked wingtip is the optimal solution when span is not constrained. It produces 2.2% better range than the second best alternative, a winglet design. When span is constrained and the same factors are considered, a winglet design is superior.

Here is what I think you need to come to your own conclusion. First I will give a very general overview over lift creation, and then I will look at three wings:

An unmodified wing
This wing plus a winglet
This wing plus the winglet, but this time folded down into the plane of the wing.

For each I will plot the lift and bending moment distribution. I will assume an elliptic circulation, fully knowing that this is not what most aircraft use. But I have to pick a distribution to make all three cases comparable, and the elliptic one makes things easier. The conclusions can be generalized for other distributions.
This will be a lengthy post (you should know me by now), so thanks to all who persevere through all of it.
Lift creation and induced drag
This topic had been covered before, and I mention it again to show a very simple and elegant way to explain induced drag that does not need vortices. I want to dispel the myth that induced drag is caused by air flowing around the wingtip, and winglets somehow magically can suppress this flow.
Consider a wing with elliptic circulation over span (think of circulation as the product of the local lift coefficient $c_l$ and local chord; it is basically the lift per spanwise increment). The wing bends the air through which it flows slightly downwards, and creates an opposite upwards force, namely lift (Newton's second law). I choose an elliptic distribution because then the downwash is constant over span, which makes the following calculations easier.

The sheet of air coming off behind the wing looks trough-shaped and moves downwards, thereby pressing other air below out of the way and allowing air above to flow inwards and to fill up the vacated volume. That is how the free vortex is created, and air flowing around the wingtips has only a small part in this.
Induced drag is the consequence of the wing bending the airflow downwards. To simplify things, let's assume the wing is just acting on the air with the density $\rho$ flowing with the speed $v$ through a circle with a diameter equal to the span $b$ of the wing. If we just look at this stream tube, the mass flow is $$\frac{dm}{dt} = \frac{b^2}{4}\cdot\pi\cdot\rho\cdot v$$
Lift $L$ is then the impulse change which is caused by the wing. With the downward air speed $v_z$ imparted by the wing, lift is: $$L = \frac{b^2}{4}\cdot\pi\cdot\rho\cdot v\cdot v_z = S\cdot c_L\cdot\frac{v^2}{2}\cdot\rho$$
$S$ is the wing area and $c_L$ the overall lift coefficient. If we now solve for the vertical air speed, we get $$v_z = \frac{S\cdot c_L\cdot\frac{v^2}{2}\cdot\rho}{\frac{b^2}{4}\cdot\pi\cdot\rho\cdot v} = \frac{2\cdot c_L\cdot v}{\pi\cdot AR}$$
with $AR = \frac{b^2}{S}$ the aspect ratio of the wing. Now we can divide the vertical speed by the air speed to calculate the angle by which the air has been deflected by the wing. Let's call it $\alpha_w$: $$\alpha_w = arctan\left(\frac{v_z}{v}\right) = arctan \left(\frac{2\cdot c_L}{\pi\cdot AR}\right)$$
The deflection happens gradually along the wing chord, so the mean local flow angle along the chord is just $\alpha_w / 2$. Lift acts perpendicularly to this local flow, thus is tilted backwards by $\alpha_w / 2$. In coefficients, lift is $c_L$, and the backwards component is $\alpha_w / 2 \cdot c_L$. Let's call this component $c_{Di}$: $$c_{Di} = arctan \left(\frac{c_L}{\pi\cdot AR}\right)\cdot c_L$$
For small $\alpha_w$s the arcus tangens can be neglected, and we get this familiar looking equation for the backwards-pointing component of the reaction force: $$c_{Di} = \frac{c_L^2}{\pi\cdot AR}$$
If the circulation over span has an elliptic distribution, the local change in circulation times the local amount of circulation is constant, and the induced drag $c_{Di}$ is at its minimum. If this would be different, a higher local $v_z$ causes a quadratic increase in local induced drag, so the whole wing will create its lift less efficiently.
Now we know we can calculate induced drag and we understand why the vortex sheet behind the wing rolls up, producing two counter-rotating vortices, all without looking at the details of the wingtip. What counts is that the wing is of finite span, so the stream tube which is influenced by the wing is of finite diameter as well. Of course, in reality there is no clear boundary between air which is affected by the wing and other air which is not. There is a diffuse transition the more one moves away from the wing.
Comparison of wingtips
First the geometries: Here are three wingtips in top and front views for comparison:

Now let's look at the circulation distribution of the simple wing tip:

Again, I choose the elliptic distribution for simplicity. The corresponding bending moment looks like that:

No surprises so far. Now we add a winglet and make it work as best as possible. This means we have to give it an angle of attack where it carries the circulation from the wing over on the winglet and completes the elliptic tapering of circulation down to 0 at the tip:

The grey dashed line is the circulation of the original wing. I adjusted the circulation such that both wings produce the same lift. $b_{WL}$ is the span at the winglet tip, and for the bending moment plot I have folded the spanwise coordinate down on the y axis:

Now the bending moment starts at the wingtip with a nonzero value. Since the sideways force of the winglet is parallel to the wing spar, this bending moment contribution is constant over span. But there is more: Now also circulation at the old wingtip location is nonzero, and we get a substantial lift increase at the outer wing stations. This effect is what causes the additional lift and gives the better aileron response that winglets make possible. But it also increases the root bending moment, because this additional lift acts with the lever arm of the outer wing.
How can we compare the induced drag of the wing with winglets to the original wing? The circulation gradient is lower, that helps. Also the diameter of that stream tube is larger, but it is hard to say by how much. The sideways force on the winglet is created by pushing the vortex sheet aft of the winglet sideways out, so the trough-shaped area should become wider. Empirical evidence hints at an increase in diameter of 45% of the winglet span (see chapter 6 for a discussion of several papers on the topic).
Just for the heck of it, let's assume that the diameter really increases in line with winglet span. Then let's compare that to the straight wing extension, where the same diameter can be assumed with much more certainty:

Now also the lift on the folded-down winglet acts upwards, so the circulation at the center of the wing can be reduced even further. However, now it adds a linearly increasing part to the bending moment, and the outer wing section creates more lift, as before with the wing with winglet:

Here, the root bending moment is higher than in the winglet case. This is a second advantage of winglets: They allow to increase maximum lift with less bending moment increase than a wing extension. But the wing extension puts all parts towards the creation of lift, and not some to the useless creation of side force. Both the extended and the winglet-wing have the same surface friction and (when we assume the same diameter of the hypothetical stream tube) the same induced drag. But since the winglet creates some side force, the remaining wing needs to fly at a higher lift coefficient. Also, the intersection of wing and winglet might be as well rounded as possible, this is where early separation starts at higher angles of attack. None of this affects the straight wing extension.
Most evidence shows that winglets improve L/D over the original wing, but folding the winglet down will more than double its effectiveness in lowering drag. Even if we assume that the winglet is just as good as an equal span extension, still the span extension comes out ahead in L/D improvement because all its lift contributes to overall lift, whereas the winglet produces a side force instead. If no separation occurs at the wing-winglet intersection, both will create the same induced and profile drag (pressure and friction), because both have the same wetted surface and the same local circulation. Again, this gives winglets the benefit of equally low induced drag, which is not supported by most measurements.
The extended wingtip in the example above has interesting characteristics. It is a sweptback (raked) wingtip, which causes the local lift curve slope to be lower than that of the straight wing. This increases its maximum angle of attack and  - assuming that the local area is bigger than what an elliptic wing shape would dictate - makes it possible to keep a nearly elliptic circulation distribution over a wider angle of attack range. The bigger local area is a sensible precaution against the wing tip stalling first, so a raked wing tip will combine benign stall characteristics and very low induced drag.
Compare this to the winglet, which has to be tailored for one polar point: Since changes in wing angle of attack will not change the incidence of the winglet, it cannot adapt as well to different flow conditions as can the extended wing. In sideslip the winglet will mess up the circulation distribution on the wingtip and will act like a deflected spoiler.
Conclusion
Comparing equal winglets and wing extensions gives these basic characteristics:

Both have the same viscous drag at low angle of attack.
Both can create more maximum lift, and both lower induced drag.
The wing extension can create most lift for the given increase in wetted surface.
The wing extension is more than twice as effective in lowering induced drag.
The wing extension gives a better circulation distribution at off-design angle of attack.
The wing extension produces the highest root bending moment for a given amount of lift.

How much the bending moment increase will drive up structural mass depends on the aspect ratio of the original wing. Low aspect ratio wings will not suffer much, but stretching high aspect ratio wings will drive up spar mass considerably. But please note that the winglet also causes higher root bending moments, and it creates less bending moment than the wing extension because it creates some side force instead of pure, useful lift.

Hi Peter, thank you very much for this interesting article. It makes all my aerodynamic classes come back from deep memory. I agree with your conclusions. It would be nice if the structural weight penalty for the additional bending moment could be quantified. Food for thought, thanks for that!

@DeltaLima: Thanks for your kind words! The structural penalty can be quantified for a particular wing, but unfortunately not in a general way.

I've been thinking about the winglet a bit more. What is the local direction of flow above the wingtip? I assume it is slightly inward as the vortex sheet starts to roll up there. This means that the lift vector of the winglet would be slightly tilted forward, causing a negative induced drag.

@DeltaLima that would be what also my fluidynamics/aerodynamics lecture notes say.
Peter so, in the absence of span restriction, basing on your conclusion, there is still no black&white answer: if you modify an existing wing, probably a winglet is better (less bending moment) [A320 style], but if you design a new wing, raked wingtip [B787]. do I read you correctly?

@DeltaLima: The winglet needs to carry over the circulation of the wing, thus creating an inward-pointing force. This deflects the airflow aft of the winglet outward, and the lift (better: Side force) vector is pointing slightly backwards, like that of the wing itself. The winglet will produce much the same drag as the span extension, but will contribute less lift.

@PeterKämpf I have a question, in the derivation of $c_{D_i}$, shouldn't you assume the small angle approach first (and dropping the tangent), before substituting $\alpha$ in $c_{D_i}=\alpha_w / 2 \cdot c_L$?
Now the factor of 0.5 went from outside to tangent to inside the tangent before using the small angle approach.

@ROIMaison: Yes, that would be cleaner. It should not matter at very small angles, though.

Looks like a slip in the latter portion - you refer to reduced L/D when describing something that increases lift and reduces drag; surely you mean increased L/D?

@anaximander: Please be more precise. The only time "reduced" occurs it refers to circulation. What precisely do you mean?

The paragraph that starts "Most evidence shows...", you say "effectiveness in lowering L/D" and "comes out ahead in L/D reduction", both in context of things that increase lift and reduce drag, which obviously increases L/D.

@anaximander: You're right, thanks for spotting this. I was probably thinking drag and wrote L/D. Corrected.

@PeterKämpf Would the weight of the winglet reduce the bending moment?

@Koyovis: Yes, the winglet weight provides a small bending relief.

Also, it was claimed that at higher $C_L$, in climb, the tip circulation creates a flow against the winglet like that of a sail boat sailing against the wind, thereby creating thrust. And that winglets mainly make sense in shorter range aircraft, which spend a larger percentage of flight time in climb.

@Koyovis: Yes, the drag reduction of winglets can be seen as caused by a wider wake or thrust on the winglet when it flies in a local sideslip. Both are correct and sides of the same medal. Their benefit grows with the fraction of induced drag on total drag. Aircraft become more efficient when flying high, close to the best L/D point on the polar, and only GA aircraft fly much faster than this because their altitude is limited. Hence, no winglets on GA aircraft.

Great answer once more!

In addition to the principles and research of other answers, here is a look at the winglet design chosen on different aircraft. Is a winglet always preferred, or only in certain circumstances?
In this answer, it is mentioned that it can make sense to add a winglet when span is restricted. Therefore, it is important to understand reasons why span may be restricted on an airliner.
Wingspan is limited structurally because bending moments place increased stress on the wing structure as the distance from the wing root increases. This means increased material and weight to handle the stress, which reduces some of the benefits of the increased span. These limits will depend on the wing structure, which varies between aircraft, so they will not be focused on here.
Wingspan is also limited by regulations. In AC 150/5300-13A by the FAA, on page 13, Table 1-2 lists six Airplane Design Groups into which aircraft are categorized based on tail height and wingspan. ICAO Annex 14 has these same groups but labeled A-F. Aside from clearance at gates and on taxiways, the group also affects other airport facilities. In most cases the wingspan is more critical than the tail height, so wingspan will be focused on here.
Group #     Wingspan (ft)
I           <49
II          49-<79
III         79-<118
IV          118-<171
V           171-<214
VI          214-<262

Below are different aircraft, and the groups in which the wingspan is categorized (values from Wikipedia). Lengths are rounded down to the nearest foot to compare against the limits. This focuses on aircraft that come with winglets as designed. Winglets available as retrofits improve performance, but the question is whether a wingspan extension would be better, which will depend on each aircraft's design.
You will see that aircraft at the upper limit of wingspan in a certain group tend to have winglets, whereas aircraft not at the limit do not. There are some exceptions to this. The LR/ER versions of the 777 reached the wingspan limit of Group V, but opted for raked tips instead of winglets. The A330/340 are below the limit of Group V but use winglets, though newer versions of the A340 do reach the limit, and all are at the upper end of the group.
An interesting case is the P-8, which is an ASW aircraft based on the 737-800. The military is less concerned with wingspan classes than commercial carriers, and endurance is an important design goal for this role. The design opted to increase wingspan and use raked tips rather than retain or add the winglets of the 737-800.
From this it seems that winglets are more useful when at a limit in wingspan. It suggests that winglets are less useful when not limited in wingspan, but is certainly not conclusive.
A380-800
Wingspan: 261 ft (Group VI)
Group Max: yes
Winglets: yes
B777-8X/9X
Wingspan: 235 ft (Group VI), fold to 212 ft (Group V)
Group Max: no
Winglets: no
B747-8
Wingspan: 224 ft (Group VI)
Group Max: no
Winglets: no
A350
Wingspan: 213 ft (Group V)
Group Max: yes
Winglets: yes
B777-200LR/300ER
Wingspan: 212 feet (Group V)
Group Max: yes
Winglets: no
B747-400
Wingspan: 211 ft (Group V)
Group Max: yes
Winglets: yes
A340-500/600
Wingspan: 208 ft (Group V)
Group Max: yes
Winglets: yes
B777
Wingspan: 199 ft (Group V)
Group Max: no
Winglets: no
B787-8/9/10
Wingspan: 197 ft (Group V)
Group Max: no
Winglets: no
A340-200/300
Wingspan: 197 ft (Group V)
Group Max: no
Winglets: yes
A330
Wingspan: 197 ft (Group V)
Group Max: no
Winglets: yes
P-8 (Based on 737-800)
Wingspan: 123 ft (Group IV)
Group Max: no
Winglets: no
A320/neo
Wingspan: 111 ft (117 ft with sharklets) (Group III)
Group Max: yes
Winglets: yes
B737 NG/MAX
Wingspan: 117 ft (with winglets) (Group III)
Group Max: yes
Winglets: yes
B737 Classic
Wingspan: 94 ft (Group III)
Group Max: no
Winglets: no
E170/175/190/195
Wingspan: 85 ft (E170/175) 94 ft (E190/195) (Group III)
Group Max: no
Winglets: yes
Less common aircraft:
SSJ 100
Wingspan: 91 ft (Group III)
Group Max: no
Winglets: no
IL96
Wingspan: 197 ft (Group V)
Group Max: no
Winglets: yes
CS100/300
Wingspan: 115 ft (Group III)
Group Max: yes
Winglets: yes

Another interesting data point to suggest that span increases are better: Boeing is going with span increases that fold up for parking on the 777X. Best of both worlds that way, I guess.

"Wingspan is also limited by regulations." The regulation is not the limitation. It is merely a formal classification which allows manufacturers, airports and possibly others to design compatible products.

So a Zeppelin-Staaken R.VI family (1917)  would be in Group IV family with the B-29.  The largest of the WWI giants would be in group V.   Just to put things in perspective.

This paper from 2005 states that is not a settled question:

When the geometric span of the wing is constrained, well-designed winglets do provide significant reductions in airplane drag and have now been incorporated on aircraft ranging from sailplanes to business jets and large commercial transports.

(and I understand you agree with the above)

The justification for winglets as opposed to span extensions for aircraft that are not explicitly span-limited is less clear. Studies at NASA Langley that compared these two concepts with constrained root bending moment concluded that winglets were to be preferred over span extensions. (Theoretical parametric study of the relative advantages of winglets and wing-tip extensions - Heyson, 1977 - NASA TP 1020). Studies with constraints on integrated bending moment suggested that the two approaches were almost identical in these respects. (Effect of winglets on the induced drag of ideal wing shapes - Jones, 1980 - NASA NASA TM 81230). A somewhat better weight model (which includes the effects of changes in wing chord on structural efficiency) leads to very similar conclusions as shown in figure 9. The conclusion is that the complexity of the structural model and constraints limits the general applicability of any such conclusions.

In particular

The evaluation of optimal winglet height and dihedral, depends on the details of the wing structure, whether the wing is gust critical or maneuver critical, whether large regions of the wing are sized based on minimum skin gauge, and whether the design is new or a modification of an existing design. The evaluation of wing tip device advantages must be undertaken for each design and include an array of multidisciplinary considerations. These include the effect on aeroelastic deflections and loads, flutter speed, aircraft trim, stability and control effects (especially lateral characteristics), off-design operation and effects on maximum lift, and finally, marketing considerations.

To conclude:

There is no clear answer to the optimal configuration, and even when winglets are adopted, the geometries vary widely.

What I understand from the above is that if you include no structural or a simple structural limitation, a winglet is better than a span extension (NASA TP 1020 referred above) otherwise you will have to search for a case-by-case answer.
There is also this other paper (behind paywall) from 2010 (5 years later than the above paper) that in its abstract reports similar conclusions:

When only aerodynamics are considered, closed lifting-surface configurations, such as the box wing and joined wing, are found to be optimal. When aerostructural optimization is performed, a winglet configuration is found to be optimal when the overall span is constrained, and a wing with a raked wingtip is optimal when there is no such constraint

if you include no structural or a simple structural limitation, a winglet is better than a span extension No, the opposite is true.

I'm guessing he's saying that without structural limitations, a span extension is preferable.

The vortices on the wingtips are not the direct cause of induced drag, they are rather sort of manifestation of it. Simply put, prolonging the wing (while keeping its structural integrity intact) would have similar result as mounting on the blended winglets. However, planes like 737NGs have to snugly fit into the wingspan limitations outlined by the ground operators. For example, P-8 Poseidon with its raked wingtips certainly posed no concerns for the military, as they do not care that much for gate dimensions or airport costs.

Yes because a winglet reduces the drag caused by the lower part of the wing comes onto the higher part of the wing and rotates forming a vortex called wing tip vortex and the winglet reduces the strength of the vortex reduces the drag also makes it more efficient and has extra range from the winglet. So its better to have a winglet than no winglet


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How efficient would an airliner be if it did not have to carry its own fuel?
Hypothetically, if all the fuel was supplied externally or pulled from the atmosphere to where the plane had never to carry any fuel on board, how much more efficient would an airliner be? The plane would not fluctuate in weight.

What exactly do you mean by "supplied externally"?

IMO this is the wrong sort of hypothetical question for the site. See: https://aviation.meta.stackexchange.com/questions/447/should-hypothetical-situations-be-addressed and https://aviation.meta.stackexchange.com/questions/3594/should-we-have-a-hypotheticals-tag-questions/3595#3595

You are certainly not asking about the max. range of such an aircraft as that would be infinite. Maybe you are asking about the hypothetical fuel burn rate at MZFW (maximum zero fuel weight), i.e. just the plane, pax, luggage, and maybe a bit of cargo? Which makes me assume that somebody would then redesignate the fuel tanks and put more cargo in there...

The less-hypothetical version of this is the nuclear powered airplane. Doesn't measurably fluctuate in weight, pretty infinite range.

I think you need to define how you measure efficiency.  Cost per mile, or fuel burned per mile?  Where you get your hypothetical fuel from will make a huge difference in these parameters.

Short answer is about twice as efficient for a mid range route,(3000 nautical miles) when based on fuel used per ton of cargo per mile traveled.
Explanation:
I will use the 737-400 as an example because I have an operational manual for it. First we need to define terms. I assume we are talking about fuel burn per something: per mile, per hour, or per payload ton-mile. Gross weight is the total weight if you set the plane on a scale in some flying condition. Max gross weight is the maximum weight at which the aircraft is considered safe to fly. Operating empty weight is the lowest gross weight achievable in a flying condition, no cargo, no extra crew or passengers, and no usable fuel. Useful load is the difference between max gross weight and operating empty weight. Payload is useful load minus fuel load and extra crew.(that is load that pays, aka cargo and passengers)
The thrust required(and thus fuel consumption) for level flight is determined by aerodynamic drag and the majority of drag is broken into parasitic drag and induced drag; parasitic drag comes from shape or texture and dynamic pressure,(basically speed if you keep the density constant) go faster get more parasite drag, this does not change with gross weight.
Induced drag is caused by the lift created by practical wing designs, for a set wing design and speed the induced drag increases with weight. So high gross weights have higher induced drag and so require more thrust.
Now for the example. A 737-400 has a maximum gross weight of 143500 pounds and a typical operating empty weight of 77100 pounds(typical airline equipment with seats and such) giving a useful load of 66400 pounds. This weight can be split up however needed between fuel and payload depending on the length of the flight.(In practice other factors can limit gross weight such as available runway length, and payload as some engineering optimizations assume a lower landing weight than takeoff weight to save on structural weight.) At least up to the limit of installed fuel tank size, this model can hold 37708 pounds of fuel.
Some reserve of extra fuel is required for safety, diversions, holding and such, so this is usually extra fuel at landing. This is typically 4000 to 9000 pounds depending on specifics of the flight.
Assuming flight altitude of 33000 feet and mach .74 cruise(430 knots). I am using nautical miles and short tons(2000 pounds) for all of this.
A the most exaggerated case will be maximum range with reserve fuel of 9000 pounds.(maximum fuel at start, reduced payload) Payload will be at most 28692 pounds or 14.3 tons. Fuel burn at the start will be 6234 pounds per hour for 1.014 pounds fuel per ton-mile of payload (6234/(14.3*430), and at the end of flight 5066 pounds per hour for 0.824 pounds fuel per ton-mile of payload (5066/(14.3*430). (geometric mean of .914 pounds fuel per payload ton-mile. Change in rate is non-linear.)
If all of the useful load could be used for payload as in the case of an external fuel supply, or an infinitely short flight with no reserve fuel, you get 66400 pounds or 33.2 tons of payload. The fuel burn will still be 6234 pounds per hour but you get .437 pounds fuel per payload ton-mile. 6234÷(33.2×430)
So cruise fuel consumption with an external fuel supply will be approximately .437/.914 = 47.8% or about half of the fuel consumed per unit of cargo. Actual results will depend on variables if I must state the obvious. Longer flights would see more improvement, shorter flights less, payloads less than maximum allowable will also see less improvement, flights requiring less reserve fuel will also see less improvement.

Airliners can typically carry about 40-45% of their maximum total weight as fuel. If they didn't need to, they could theoretically carry that much extra payload instead, or they could fly lighter and burn 40-45% less fuel (because fuel burn rate is closely related to the total weight).
Obviously it's not quite that simple. Planes usually only carry as much fuel as they need (plus a safety margin), and they burn fuel as they fly, so the fuel weight is almost zero at the end of a flight. That would at least halve the improvement, so say 20%.
This assumes that you magic fuel either weighs nothing, or you're somehow teleporting it to the engines from the ground, or air-to-air refuelling where you don't count the cost of the tanker. And that you're only interested in fuel burned, not cost, because there's no way the estimate the cost of hypothetical magic :-)

There are several answers, depending on what precisely your idea of zero fuel means.
The first is the simplest: We use a regular aircraft and simply assume that it takes off with zero fuel and still flies as if its tanks are full. Now the answer depends on the range: Longer flights need disproportionally more fuel. The linked answer gives 3.88% of landing mass per 1000 km for 2000 km range but 4.16% per 1000 km for a flight over 5700 km. The benefit is obviously highest for intercontinental traffic. If you now consider that ultra-long range flights are only possible with a fraction of the potential full passenger load, the increase in efficiency would be up to a factor of 4.
This splendid answer contains a table which lists how much more fuel is used to carry fuel along for a trip exceeding 2800 nautical miles. As you can see, extending the flight to 8000 miles needs 12% of the fuel load only to carry the extra fuel.
A more refined answer would also include the mass and volume requirements for the tanks. If the airliner is designed without fuel mass and volume in mind, it could be smaller and lighter (not counting that magical fuel-catching device, of course). Wings could have a higher aspect ratio and systems could be simpler. Parametric formulas for the tank mass estimate fuel tanks to weigh about 6.4% of the fuel they contain and wing tanks 1.8% on a basis of 20 tons (the percentage gets smaller with bigger tanks) plus a contribution in kg that is proportional to 23% of static thrust given in kN. Leaving out the tanks will increase payload by about 0.8% of total mass and allow for a slightly better L/D. Relative to payload mass which is between 30% on short and 10% on long range flights the mass savings alone add another 2.4 to 8% to efficiency.
In total, the gain in efficiency is likely to be about 5% for very short range and 15% to 25% for long range flights as long as take-off mass does not limit the payload which can be carried and the tank mass is included in the calculation.

...how much more efficient would an airliner be?

Answer: $$ \frac {\text{fuel weight percentage at TO - fuel weight percentage at touchdown}}{2}$$
This answer computes the saving in fuel consumption due to a saving in empty weight - 10% less empty weight results in a fuel saving of 10%.
That is empty weight. In a traditional, fuel burning aeroplane, total weight decreases linearly over time due to using fuel. So fuel saving due to used fuel weight saving decreases linearly over the duration of the flight as well.
Let's take a B777-300ER for example:

OEW = 167,829 kg
MTOW = 351,533 kg
Fuel capacity = 145,538 kg

If the plane takes off at MTOW with maximum fuel on board, the fraction of fuel weight = 145,538/351,533 = 41.4%. If at touchdown there is no more fuel left, fuel weight fraction = 0%. Total average fuel savings over the duration of the flight = (41.4 -0)/2 = 20.7%.
A normal B777-300ER would burn 145,538kg of fuel. A magic fuel accumulating B777ER would burn (1 - 0.207) * 145,538 = 115,410 kg of fuel. It is 20.7% more efficient.


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What is the rule of thumb for land/taking-off on a sloped runway?
Skyvector lists the gradient for KMCI as 0.3%.  What is the rule of thumb for how large a gradient needs to be before you always take off downhill and always land uphill like they do at Lukla?  Assume winds are not a factor.

actually the reason for only taking off in one direction is terrain. you won't be able to drop to the tarmac after clearing the hill behind it

A runway with an uphill grade is equivalent to a shorter runway with no grade. You might ask in Physics for the formula.

@ratchetfreak: Well, VNLK has 12% gradient and that is itself steeper than both descent and climb gradient of most planes, considering the 9 200 ft altitude.

12% is 6.875 degrees! http://www.wolframalpha.com/input/?i=12%25+in+degrees

What does your POH/AFM says?
Ignoring winds and other factors, it depends on effective runway length, not just runway length. If you have a runway long (really long) enough, you can takeoff/land in either direction.
As mentioned here:

... advantage or disadvantage of a sloped runway is that a 1% runway
  gradient — an increase or decrease in altitude of 10’ for every 1000’
  of runway length — is equivalent to a 10% increase or decrease in
  effective runway length ...

Example:
Runway length is 1500' with 3% up-slope gradient

Landing uphill on it will give us an effective runway length of almost 2000’ (1500’ x 1.3 = 1950’).
Landing downhill on it will give us an effective runway length of just over 1000’ (1500’ x 0.7 = 1050’).

Just for reference, the runway (6: uphill; 24: downhill) at Lukla Airport has 12% gradient and is 1500' long.
Effective Runway Lengths (using the formula above)
 6: 1500' x |(1+1.2)| = 3300'
24: 1500' x |(1-1.2)| =  300'

Hence, hypothetically speaking, if runway 24 is 48,400' long with no wind, A380 can takeoff too.

Except that you can't land downhill on anything steeper than your descent gradient at all. And you can't take-off uphill from anything steeper than your climb gradient at all either. And in multi-engine you obviously wouldn't attempt to take off uphill steeper than your one engine inoperative climb gradient. Normal descent gradient is 5%, Lukla has 12% (and Courchevel has 18%).

@JanHudec Good Point. That's why I said hypothetically, not theoretically or practically. Even with no wind, there are many other factors too. I also started the answer with Ignoring winds and other factors....

By the way, how do you justify the absolute value? The rule does not say any such thing. The effective length for takeoff on 10% uphill/landing 10% is 0 according to the rule and for steeper gradient it therefore should be negative (so it is minus 300' for landing on VNLK 24)

@JanHudec I did that because length is a scalar quantity, but I do agree with your example.

I happened to be looking at some takeoff distance charts, so I looked into this. As Tyler says, the answer will depend on your airplane's performance. With good brakes and plenty of runway, a small plane may not care as much as a larger one. The following applies to the PC-12.
I know you said to assume winds are not a factor, but it may help to roughly relate the effects of slope and wind. It turns out that 4% of slope will either help or hurt about the same amount as 10 kt of wind (within about 7%). Both provide around 10% benefit or 25% penalty on takeoff distance, and landing distance is affected by slope a bit less and wind a bit more. This would provide a good sense of how much a slope will affect the runway length you need. That penalty will certainly start to hurt as slope increases.

There is no firm guideline. It depends on wind conditions and other factors like the surrounding terrain.
I have landed at Jaffrey only uphill, which has a 0.9% grade and a bad surface, but people can and do land there downhill. It is very steep for an air strip. If the wind was strong enough I would have no problem landing downhill there, but with moderate winds I would always go uphill.

OP wrote "Assume winds are not a factor."

Well, if there is no wind and no terrain you would normally land uphill on a graded runway if it has a listed gradient.

OP wanted to know how a grade figures into the aeronautical decision-making to land downhill or take off uphill, and if there's a rule-of-thumb. for example, runway 01 is 2500 feet long and downhill, and you're approaching from the south. Would you make a straight in, or circle at .5%? 1%? 5%?


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Two- and three-wheel undercarriage in the same airplane?
Are there any airplane types which have the capacity to land in a tricycle configuration and a tail dragger configuration in consecutive landings? I have one example in mind but wonder whether there are more. Different versions of the same type don't count; it should be the same airplane without structural changes between landings.

Wouldn't that require a change in the center of gravity between landings? I know I can take the tail of my 177 and push it all the way to the ground and it very much wants to pop back up to tricycle configuration. I'd hate to be flying a plane that can't decide if it's a tail dragger or a tricycle during landing...

What airplane do you have in mind? To Ron's point, it can either sit on its nose or sit on its tail in the end.  You could design it with a tail wheel and a nose wheel and make ground contact with either during a landing, but depending on main gear placement, you still end up with a trike with a wheeled tail skid, or a taildragger with an "anti-prop strike safety caster" up front.

@RonBeyer Think outside of the box.

@JohnK That description would fit the Zeppelin Staaken giant airplanes. I actually didn't think of those, but they would also be a good answer.

@JohnK That reminds me of Concorde, which had a fourth wheel at the tail to protect the trim tank located there, but AFAIK they did not usually land on that wheel.

@JohnK Some aircraft do change configuration significantly though I've checked though I thought this wasn't the answer, but consider the shuttle carrier aircraft.  That had a very different mass distribution with/without the orbiter (solved by ballast in that case).  The White Knight launch planes also don't fit - I think the CoG changes less anyway, but they do it in flight.  Or the V22 which (I think) can land in 2 very different configurations - but there's no sign of a tailwheel.  That would be closer to your last sentence

I think what @PeterKämpf has in mind is a retractable main gear that can be extended angled forward or extended angled back so the tires can be placed ahead (TD mode) or behind (Trigear mode) the C of G as the pilot chooses.  Or even the same sort of feature with a fixed gear with a fore/aft actuation system.  It would have to be for a mission purpose where the need to switch configurations is worth the weight/drag/complexity penalty.

@JohnK interesting - I was considering the CoG moving with respect to the airframe (and therefore wheels) because of operational necessity, but the wheels could move too.  But many reasons to have the tail low to the ground (like a ramp) would also restrict a tailwheel

Indirectly related, but gear placement is a big problem on tail-engined jets.  If the gear was at the optimal location to sit level when loaded while requiring the minimum tail down force for rotation, the plane would need a tail strut to hold the back up when the cabin was unloaded.  The gear has to be placed farther aft to avoid this, which then needs a larger elevator surface to get enough tail power for rotation with the higher moment caused by the aft wheel footprint. One of the reasons tail mounted engines are less common on airliners.

Well, there are some gliders that have a small nosewheel, and a larger main wheel, and a tailwheel.  At normal CG position they will eventually come to stop with the nosewheel on the ground, but could  be landed with the  tailwheel touching first and rolling for a while before the glider settles down in a nosewheel-down position, or could be landed w/o tailwheel ever touching.  So that's kind of the same concept as you seem to be asking about?  See https://en.wikipedia.org/wiki/Grob_G103a_Twin_II#/media/File:G103_Twin_II_landing.jpg , https://en.wikipedia.org/wiki/Grob_G103a_Twin_II

Do some tailhooks for carrier landings incorporate a small wheel?

The Fairchild A-10 has been designed with a lot of forethought, taking resilience against possible battle damage into account. If half of the tail is lost, the other half is sufficient to fly home. Also, if the gear cannot be lowered, the tires are still oriented the right way and stick out of the wheel wells enough so the airplane will land on them. Since the gear retracts forward, the wheels are ahead of the center of gravity in their retracted position, turning what is a tricycle undercarriage into a taildragger with gear retracted.
As reported here:

When retracted, the Thunderbolt II's main landing gear wheels remain partly exposed: During a belly landing, depending on the stores carried by the aircraft, the wheels that partially protrude from their nacelles can provide a cushion to absorb the impact with the runway; they can also reduce the risk of fire and, generally speaking, the overall damage to the fuselage.
In addition, when the gear is up, the wheels continue to guarantee the braking action, allowing the pilot to control the aircraft through differential use of the wheel brakes. That's why the MLG design is one the features that make the iconic aircraft so resilient.

Of course, it is prudent to drop all external stores before attempting this.

An A-10 Thunderbolt II sits on the runway after making an emergency landing March 25, 2008, at Edwards Air Force Base, Calif. (picture source). This view also illustrates nicely how the pulled-down wingtips will protect the ailerons from involuntary ground contact.

It lacks a tail wheel, so it literally drags its tail on the runway, causing significant damage to the underside of the vertical stabilizers. I estimate approximately 20 cm of fin is missing.

I nominate the Concorde. Although it would always end up taxiing in tricycle configuration, it could definitely land as a tail dragger.

Source: Wikipedia, photo by El Grafo